SAT Math — Algebra Quick Reference

Core Concepts

Solving Linear Equations

|---|---| Word problem translation: |---|---| Interpreting linear equations in context:

• Coefficient of x (slope) = rate of change (cost per unit, speed, etc.)

• Constant term (y-intercept) = starting value (flat fee, initial amount)

Systems of Equations

|---|---| Number of solutions: |---|---| Real-world setup tip: Define variables → Write 2 equations → Solve

Linear Functions (Slope-Intercept Form: y = mx + b)

|---|---|

Step	Action
1	Distribute (clear parentheses)
2	Combine like terms on each side
3	Move variables to one side
4	Move constants to other side
5	Divide by coefficient
English	Math
"is / equals / results in"	=
"more than / increased by / sum of"	+
"less than / decreased by / difference"	−
"times / product of / of"	×
"per / divided by / ratio"	÷
"a number / the unknown"	x
Method	Best when...
Substitution	One equation already has a variable isolated
Elimination	Coefficients can be made equal with multiplication
Situation	Result
Different slopes	One solution (lines intersect)
Same slope, different y-intercept	No solution (parallel lines)
Same slope, same y-intercept	Infinite solutions (same line)
Term	Meaning
m (slope)	Rate of change; rise/run; (y₂−y₁)/(x₂−x₁)
b (y-intercept)	Starting value; y when x = 0
Positive slope	Line rises left to right
Negative slope	Line falls left to right
Zero slope	Horizontal line
Undefined slope	Vertical line

Writing a line from a point and slope:

y = mx + b

Substitute (x, y) from the known point and the slope m

Solve for b

Parallel lines: Same slope, different y-intercept Perpendicular lines: Slopes are negative reciprocals (m₁ × m₂ = −1)

Common Exam Traps

• Intervening phrase tricks: "The cost of 5 items, plus tax, ___" — tax is the extra constant, not part of the 5x

• "Less than" vs. "is less than": "5 less than x" = x − 5 (not 5 − x)

• Elimination setup: Make coefficients equal AND opposite before adding

• Infinite solutions: One equation must be a multiple of the other

• Slope from graph: Rise is vertical change, run is horizontal — not the other way around

• Interpreting context: Always ask "what does x represent?" before interpreting slope and intercept

• Parallel vs. perpendicular: Parallel = same slope; perpendicular = negative reciprocal slope